Your best bet would be to contact Arizona Game and Fish.
2221 W. Greenway Rd.
Phoenix, Arizona 85023
(602) 942-3000
Or, in this day and age:
www.azgfd.com
The following numbers are for the 2000-2001 season. The new regulations stating rule changes and possible increases in fees will come out shortly with a supplement for other late season species being published in September (javelina, bear). Be sure to request that you be placed on a mailing list to get your copy. Also be sure to request a few applications, in case you goof yours up (I NEVER do that...).
First, each hunter must have the requisite license.
$25.50 - resident general hunting license (Class G)
$ 113.50 - Non-resident general hunting license (Class G).
Tag fees by species (required by each person and for for each species you are drawn to hunt in addition to the license):
Deer - $22.50/$113.50
Deer (Kaibab region) - $27.50/$118.50
Elk - $76.50/$371.00
NOTE: first number is the resident fee, second number is the non-resident fee.
For example, if you want to hunt deer as a non-resident, the total cost would be $227. For a resident, the same hunt would be $48. This is per person, as each are required to have both a hunting license and a tag. Pretty typical.
Hunts are done by lottery via computer drawings.
All fees are refunded (except for a $5.00 processing fee per hunt applied for) if you are not drawn. Up to four people may apply for a hunt on the same application and both the license and tags can be purchased on the same application. You may apply for up to 5 hunts per application. Hunts are numbered and identify the time period and area in addition to the selected game.
Deadline for applications is June 12 (this year, anyway) by 7PM. Only one application per species is permitted. Application may be mailed or hand-delivered only. Postmarks don't count. Get it in on time. They have NO sense of humor on deadlines.
Getting drawn is quite competitive, especially for elk.
Getting drawn as a non-resident seems to be a lot easier than as a resident, anymore.
After a continued unlucky spell, one of my hunting buddies was complaining to his neighbor. The neighbor had been drawn for elk 5 years running without fail. When my buddy quizzed him how that could be possible, the neighbor said he simply applied as a non-resident. My buddy asked him to explain how that was possible. The neighbor said to look at the fees involved, especially for elk.
Can't say there is something afoot, but economics can be tough, especially in a state with such a huge budget shortfall.
I am sure that Arizona Game and Fish can answer your questions better than I can, but if you have any specifics you can always e-mail me.
Good hunting.